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Dr Harvey Stern,

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Dr Harvey Stern, Climate Manager, Victoria and Griffith University Mr Glen Dixon, Associate Lecturer (Finance), Brisbane Introduction Evidence of the challenge faced ... – PowerPoint PPT presentation

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Title: Dr Harvey Stern,


1
  • Dr Harvey Stern,
  • Climate Manager, Victoria
  • and

Griffith University
Mr Glen Dixon, Associate Lecturer (Finance),
Brisbane
2
4th Annual Tasmania Power 2002,Energy Risk for
Tasmania Master ClassHobart 9-11 April 2002
Application of Weather Derivatives to the
Tasmanian Market
3
Introduction
  • Evidence of the challenge faced by the
    meteorological community to become skilled in
    applying risk management products from financial
    markets is growing.
  • An empirical approach to the pricing of weather
    derivatives is presented. The approach is
    illustrated with several examples.

4
Background
  • It is the energy and power industry that has, so
    far, taken best advantage of the opportunities
    presented by weather derivatives.
  • Indeed, the first weather derivative contract was
    a temperature-related power swap transacted in
    August 1996.

5
Weather Derivatives Defined
  • Clewlow et al...(2000) describe weather
    derivatives as being similar "to conventional
    financial derivatives, the basic difference
    coming from the underlying variables that
    determine the pay-offs", such as temperature,
    precipitation, wind, heating degree days, and
    cooling degree days.

6
Defining Cooling Degree Days
  • Number of cooling degree days during a season is
    the accumulated number of degrees the daily mean
    temperature is above a base figure, usually 18
    deg C.
  • Number of cooling degree days might be regarded
    as a measure of the requirement for cooling.

7
Defining a CoolingDegree Day Call Option
  • Strike 600 cooling degree days.
  • Notional 100 per cooling degree day (above
    600).
  • If, at the expiry of this contract, the
    accumulated number of cooling degree days is
    greater than 600, then the seller of the option
    pays the buyer 100 for each cooling degree day
    above 600.

8
Pay-off Chart for the CoolingDegree Day Call
Option
9
Pricing Approaches
  • Historical simulation.
  • Direct modeling of the underlying variables
    distribution.
  • Indirect modeling of the underlying variables
    distribution (this involves simulating a sequence
    of data).

10
Defining a 38 deg C Call Option(assuming a
temperature of at least38 deg C has been
forecast)
  • Location Melbourne.
  • Strike 38 deg C.
  • Notional 100 per deg C (above 38 deg C).
  • If, at the expiry of this contract (tomorrow),
    the maximum temperature is greater than 38 deg C,
    the seller of the option pays the buyer 100 for
    each 1 deg C above 38 deg C.

11
Pay-off Chart for the38 deg C Call Option
12
Determining the Price of the38 deg C Call Option
  • Between 1960 and 2000, there were 114 forecasts
    of at least 38 deg C.
  • The historical distribution of the outcomes are
    examined.

13
Historical Distribution of Outcomes
14
Evaluating the 38 deg C Call Option (Part 1)
  • 1 case of 44 deg C yields (44-38)x1x100600
  • 2 cases of 43 deg C yields (43-38)x2x1001000
  • 6 cases of 42 deg C yields (42-38)x6x1002400
  • 13 cases of 41 deg C yields (41-38)x13x1003900
  • 15 cases of 40 deg C yields (40-38)x15x1003000
  • 16 cases of 39 deg C yields (39-38)x16x1001600
  • cont.

15
Evaluating the 38 deg C Call Option (Part 2)
  • The other 61 cases, associated with a temperature
    of 38 deg C or below, yield nothing.
  • So, the total is 12500.
  • This represents an average contribution of 110
    per case, which is the price of our option.

16
Defining a Cooling Degree Day Put Option
  • Strike 600 cooling degree days.
  • Notional 100 per cooling degree day (below
    600).
  • If, at the expiry of this contract, the
    accumulated number of cooling degree days is less
    than 600, then the seller of the option pays the
    buyer 100 for each cooling degree day below 600.

17
Pay-off Chart for the Cooling Degree Day Put
Option
18
A Forecast Error Put Option (defining error as
predicted minus observed)
  • Strike 0 deg C.
  • Notional 100 per degree of forecast error below
    0 deg C
  • If the forecast underestimates the actual
    temperature, then the seller of the option pays
    the buyer 100 for each 1 deg C of
    underestimation.

19
Evaluating theForecast Error Put Option
  • Historical simulation yields a suggested price of
    67 for our put option.
  • Two questions
  • Does todays error influence the price?
  • Does tomorrows expected weather pattern
    influence the price?

20
Answering the First Question
  • Todays error does influence the price
  • If todays forecast is an underestimate, then
    tomorrows is also likely to be an underestimate,
    leading to a suggested option price of 75.
  • If todays forecast is an overestimate, then
    tomorrows is also likely to be, leading to a
    suggested option price of 41.

21
Answering the Second Question
  • Tomorrows weather pattern does influence the
    price, for example
  • If tomorrows weather pattern is moderate
    anticyclonic NNE, tomorrows forecast is likely
    to be an underestimate, leading to a price of
    77.
  • However, if tomorrows weather pattern is strong
    anticyclonic NNE, tomorrows forecast is likely
    to be an overestimate, leading to a price of 47.

22
A Monthly Rainfall Decile 4Put Option for Echuca
  • Strike decile 4
  • Notional 100 per decile below decile 4.
  • If, at the expiry of this contract, the rainfall
    decile is less than 4, then the seller of the
    option pays the buyer 100 for each decile below
    4.
  • Note Decile 1 is a rainfall total in the lowest
    10 of historical records, decile 2 is in the
    second lowest, decile 3 is in the third lowest,
    etc.

23
Pay-off chart for the Monthly Rainfall Decile 4
Put Option
24
Historical Distribution of Outcomes (for cases
when the Southern Oscillation Index is in the
lowest 3 deciles - an indicator of dry conditions)
25
Evaluating the Decile 4 Put Option(for cases
when the Southern Oscillation Index is in the
lowest 3 deciles)
  • 9 cases of Decile 1 yields (4-1)x9x1002700
  • 6 cases of Decile 2 yields (4-2)x6x1001200
  • 4 cases of Decile 3 yields (4-3)x4x100400
  • The other 25 cases (Decile 4 or above) yield
    nothing.
  • leading to a total of 4300, and an average
    contribution of 98, which is the price of our
    put option.

26
Evaluating Other Derivatives
  • An experiment is conducted to illustrate the
    importance of mean reversion and jumps in the
    evaluation of other financial derivatives.
  • Mean reversion and jumps are features of the
    Monte Carlo approach to modeling weather
    derivatives.

27
The Experiment
  • It is assumed that stocks are purchased following
    a break in an extended sequence of consecutive
    price falls.
  • It is assumed that stocks are short-sold
    following a break in an extended sequence of
    consecutive price rises.
  • Net returns are determined.

28
Mean Reversion
  • Mean reversion is demonstrated by
  • The average return being 4.51 with a standard
    deviation of 12.15 yielding the result-
  • The average is different from zero at the 0.1
    level of significance, the ve return reflecting
    the operation of mean reversion.

29
Jumps
  • The operation of jumps is illustrated in the next
    slide, which presents the ratio
  • (frequency of returns from experiment)
  • (frequency of returns if distribution normal)
  • that ratio being presented in half standard
    deviation steps from the mean.

30
The Ratio(note the much higher frequency of
extreme returns)
31
The ratio(without the extreme cases)
32
Concluding Remarks
  • An empirical approach to the pricing of weather
    derivatives has been presented.
  • The approach utilises a range of data types to
    price weather derivatives, including forecast
    accuracy data.
  • It has been shown that mean reversion and jumps,
    features of the Monte Carlo approach to the
    modeling of weather derivatives, should also be
    included in the modeling of other derivatives.
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